Experiments with proof plans for induction
Journal of Automated Reasoning
Coloring Terms to Control Equational Reasoning
Journal of Automated Reasoning
Incresing the Versatility of Heuristic Based Theorem Provers
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
Experiments in Automating Hardware Verification Using Inductive Proof Planning
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Higher-Order Annotated Terms for Proof Search
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Isar - A Generic Interpretative Approach to Readable Formal Proof Documents
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Logic Program Synthesis in a Higher-Order Setting
CL '00 Proceedings of the First International Conference on Computational Logic
The Use of Explicit Plans to Guide Inductive Proofs
Proceedings of the 9th International Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
The Use of Proof Plans to Sum Series
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
System Description: Proof Planning in Higher-Order Logic with Lambda-Clam
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Rippling: meta-level guidance for mathematical reasoning
Rippling: meta-level guidance for mathematical reasoning
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
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Rippling is a form of rewriting that guides search by only performing steps that reduce the differences between formulae. Termination is normally ensured by a defined measure that is required to decrease with each step. Because of these restrictions, rippling will fail to prove theorems about, for example, mutual recursion where steps that temporarily increase the differences are necessary. Best-first rippling is an extension to rippling where the restrictions have been recast as heuristic scores for use in best-first search. If nothing better is available, previously illegal steps can be considered, making best-first rippling more flexible than ordinary rippling. We have implemented best-first rippling in the IsaPlanner system together with a mechanism for caching proof-states that helps remove symmetries in the search space, and machinery to ensure termination based on term embeddings. Our experiments show that the implementation of best-first rippling is faster on average than IsaPlanner's version of traditional depth-first rippling, and solves a range of problems where ordinary rippling fails.